Khan.scratchpad.disable(); For every level Luis completes in his favorite game, he earns $470$ points. Luis already has $210$ points in the game and wants to end up with at least $2640$ points before he goes to bed. What is the minimum number of complete levels that Luis needs to complete to reach his goal?
To solve this, let's set up an expression to show how many points Luis will have after each level. Number of points $=$ $ $ Levels completed $\times$ Points per level $+$ Starting points Since Luis wants to have at least $2640$ points before going to bed, we can set up an inequality. Number of points $\geq 2640$ Levels completed $\times$ Points per level $+$ Starting points $\geq 2640$ We are solving for the number of levels to be completed, so let the number of levels be represented by the variable $x$ We can now plug in: $x \cdot 470 + 210 \geq 2640$ $ x \cdot 470 \geq 2640 - 210 $ $ x \cdot 470 \geq 2430 $ $x \geq \dfrac{2430}{470} \approx 5.17$ Since Luis won't get points unless he completes the entire level, we round $5.17$ up to $6$ Luis must complete at least 6 levels.